## Electronic Structure: Basic Theory and Practical MethodsThe study of the electronic structure of materials is at a momentous stage, with the emergence of computational methods and theoretical approaches. Many properties of materials can now be determined directly from the fundamental equations for the electrons, providing insights into critical problems in physics, chemistry, and materials science. This book provides a unified exposition of the basic theory and methods of electronic structure, together with instructive examples of practical computational methods and real-world applications. Appropriate for both graduate students and practising scientists, this book describes the approach most widely used today, density functional theory, with emphasis upon understanding the ideas, practical methods and limitations. Many references are provided to original papers, pertinent reviews, and widely available books. Included in each chapter is a short list of the most relevant references and a set of exercises that reveal salient points and challenge the reader. |

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### Contents

Overview and background topics | 1 |

Overview | 11 |

Theoretical background | 52 |

Periodic solids and electron bands | 73 |

Uniform electron gas and simple metals | 100 |

Density functional theory | 119 |

The KohnSham ansatz | 135 |

Functional s for exchange and correlation | 152 |

Wannier functions | 418 |

Polarization localization and Berrys phases | 434 |

Locality and linear scaling ON methods | 450 |

Where to find more | 475 |

Basic definitions and variational equations | 476 |

Appendix E Dielectric functions and optical properties | 492 |

Smeared nuclei or ions | 505 |

Surface and interface dipoles | 507 |

Solving KohnSham equations | 172 |

Important preliminaries on atoms | 187 |

Pseudopotentials | 204 |

the three | 233 |

full calculations | 254 |

tightbinding | 272 |

full calculations | 298 |

APW KKR MTO | 313 |

linear methods | 345 |

Predicting properties of matter from electronic | 369 |

phonons magnons | 387 |

Excitation spectra and optical properties | 406 |

Stress from twobody pairwise forces | 514 |

Energy density | 520 |

Alternative force expressions | 529 |

Appendix J Scattering and phase shifts | 536 |

Chebyshev polynomials | 542 |

Iterative methods in electronic structure | 553 |

K Exponential projection in imaginary time | 564 |

Appendix N Code for empirical pseudopotential and tightbinding | 570 |

References | 576 |

618 | |

### Common terms and phrases

algorithm applied approach approximation atoms bands basis functions Bloch Brillouin zone calculations cell condensed matter core correlation Coulomb crystal defined denotes density functional theory density matrix derived described dielectric dielectric function effects eigenstates eigenvalues electronic structure example exchange exchange-correlation excitations Exercise expressions Fermi energy Fermi surface Figure finite formulation given Green's function grid hamiltonian Hartree Hartree-Fock Hohenberg-Kohn independent-particle integral interactions iterative kinetic energy Kohn-Sham equations lattice leads linear LMTO localized logarithmic derivative many-body matrix elements metals methods minimization molecules non-interacting non-local norm-conserving nuclei operator orbitals orthogonal particles perturbation phase phonon Phys Physics plane waves polarization potential problem properties pseudopotential quantum radial relation response function Schrodinger equation self-consistent semiconductors Show shown in Fig simple solids solution space sphere spherical spin stress symmetry tight-binding tight-binding model total energy transformation valence variational vectors Wannier functions wavefunction

### Popular passages

Page 602 - VR Saunders, R. Dovesi, C. Roetti, M. Causa, NM Harrison, R. Orlando, CM Zicovich-Wilson, CRYSTAL98, User's Manual, University of Torino, Torino, 1998.